Lifetime imaging

Time-Correlated Single-Photon Counting (TCSPC) technique was used to discriminate SHG from TPPL, both emitted by the gold structures.37,53 The setup for TCSPC was distinct from that of SHG microscopy and was based on a Leica SP2 microscope coupled to a single-photon counting module (PicoQuant-PicoHarp 300). The excitation source was a Ti:Sa laser emitting 150 fs pulses. The input polarization was fixed and set to the y direction with respect to the structures. The excitation wavelength was set to 800 nm. The temporal distribution of the counted photons at 400 nm of the emission wavelength was fitted by a single exponential function, 𝐼𝐼_𝑡𝑡 =𝐼𝐼₀exp(−𝑡𝑡/𝜏𝜏), where 𝜏𝜏 stands for the time constant associated with the lifetime of the excited state. For TPPL measurements a low- pass filter was used to eliminate all photons with wavelengths above 750 nm, while for SHG measurements a narrow band-pass filter centered at 400 nm (bandwidth 10 nm) was added.

4.3 Results and discussion

The SEM images shown in Figure 4-1 represent the sets of triangular gold nanoprisms used in this study. The experimental normalized and non-polarized extinction spectra of the investigated structures for gap distance varying from 0 nm to 100 nm are shown in Figure 4-3a. We clearly see from this figure that the extinction spectrum maximum shifts to the blue spectral range with increasing distances between gold nanoprisms from 0 nm to 100 nm by 25 nm step, which is a signature of the localized surface plasmon (LSP) coupling. The large spectral widths of the collected spectra are mainly due to the very short lifetime of plasmon excitations that results from very large ohmic losses. In the case of gold, these losses are larger at shorter wavelengths due to the interband transitions. Inhomogenous effects due to the variability of the structure geometry is also a source of spectral broadening.

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simulations of the extinction spectra for the same gold triangular prism configurations with the same gap distances for an excitation wavelength spectral range varying from 500 nm to 900 nm (Figure 4-3b).

Figure 4-3: Normalized measured (a) and calculated (b) extinction spectra of the triangle patterns shown in colors for different gap distances. (c) Effect of the angle

rounding on the calculated extinction spectra for patterns with a 100 nm gap.

The simulated results show good agreement with the experimental results, the same extinction spectrum maximum blue shift and similar spectrum profiles, except for the structure with no gap. In the case of gap-less structures, the discrepancy between the real

721 Wavelength / nm E x ti n c ti o n / a . u . E x ti n c ti o n / a . u . E x ti n c ti o n / a . u .

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experimental measurements and theoretical simulations, we observe the spectral broadening with decrease of the gap size between nanoprisms due to the coupling of plasmon resonances between single individual prisms. The absence of such spectral broadening at the blue spectral edge of the experimental extinction spectra is probably linked to experimental conditions: lower optical transmission in the visible spectral range as well as a lower detector sensitivity in this range. The observed tendency of the

extinction spectrum change, namely a red shift, emitted intensity increase and spectrum broadening with decrease of the gap, results from an increase of the local free electron density concentration. Further consequences are lower plasmon resonance frequencies and higher emitted intensity due to the increased number of emitting oscillators. The broadening of the spectrum is then a result of the increased probability of involvement of higher order oscillating modes.54 In FDTD calculations, it was crucial to round-off the apices of the individual triangles as shown in Figure 4-1 to closely reproduce the features of the e-beam fabricated samples. The impact of apices rounding is demonstrated in Figure 4-3c for nanoprisms structures with a 100 nm gap. The experimental result (red line) corresponds well to the simulated one for the cases of rounded angles (blue line). The simulated extinction curve for the case of the sharp angles (green line) is red-shifted by 66 nm with respect to the experimental curve (λmax=720 nm). The results of

simulation for sharp angles give the maximum of extinction spectrum at λmax=786 nm

while after rounding the apices, the extinction spectrum maximum shifts to λmax=732 nm.

Both, the experimental and the simulation results demonstrate the location of the

extinction maximum in the 700-800 nm spectral region that varies in function of the gap width between the triangular nanoprisms. The obtained results clearly define the region of LSPRs that are important towards further structure investigation with methods of nonlinear optical spectroscopy and microscopy. These results evidence a strong

dependence on sample geometry and on the distance between the investigated triangular nano-prisms.

To further probe the structures comprising three gold triangular nano prisms with variable gap sizes, second-harmonic generation measurements were performed using a tunable

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structures was collected for an excitation wavelength varying between 750 and 960 nm and detected with two calibrated APDs assigned to the detection of the p and s polarized SHG as depicted in Figure 4-2 and further detailed in the experimental methods section. The integrated SHG signal was collected by raster-scanning a defined surface and then averaging the collected signal.

The variation of SHG intensity as a function of the excitation wavelength is shown in Figure 4-4 for a 100 nm gap distance. When approaching the LSPR maximum at 720 nm the SHG emission is strongly enhanced and is already one order of magnitude higher at 770 nm as compared to the SH intensity at 900 nm.

Figure 4-4: SHG spectrum of the set of three triangular gold nanoprisms with a 100

nm gap. The average excitation power was kept constant (50 µW) at the entrance of

the microscope. The laser beam polarization was kept linear along the x-axis as depicted in Figure 4-1. The SHG spectrum was obtained by averaging the signal

collected over a selected area. The SHG spectrum was corrected for the output optics transmission and for the APD’s quantum efficiency.

0 5 106 1 107 1.5 107 2 107 750 800 850 900 950 1000 S H G s ig n a l Wavelength nmλexc /

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wavelength is matching the LSPR wavelength. Noticeably a weaker resonance is also observed for an excitation at 850 nm. This later resonance appears critical for the polar measurements performed on these structures. These measurements provide strong evidence for the coupling of second harmonic generation with localized surface plasmon excitation, opening the way to generating the desired SH signal by tailoring of the sample structure.

In order to investigate the nonlinear properties, polarization resolved two-photon confocal microscopy was used to spatially map the SHG response and measure the polarized patterns from individual nano-prisms.51,52 Such mapping is done using point- by-point scanning with 20 nm steps along the x and y directions with image

reconstruction based on the number of photons collected by the APDs. Examples of SHG images collected at 390 nm of some of the studied samples are shown in Figure 4-5 a-d. The nonlinear optical microscopy experiment provides enhanced spatial resolution that allows to distinguish signals from the individual triangular prisms as shown in Figure 4-5 a-d for small gaps with dimensions below 100 nm.55 For a low excitation average power of 50 µW (λ=780 nm) at the sample, the signal originates from regions where SHG is enhanced through plasmon coupling. Such regions are characterized by their higher free electron density which increases the local electric field and therefore accounts for the onset of local peaks in the emitted SHG intensity. Both sets of prisms in Figure 4-5a clearly show three spots that confirm that the signal originates from triangle apexes.

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Figure 4-5: a) SHG image of two sets of non-centrosymmetric gold structures. For each set of three triangular nanoprisms (200 nm base dimension), the gap between the individual prisms was 100 nm. b) A larger region of sets of the triangular gold nanoprisms with 50 nm gap between nanoprisms. Each triangular nanoprism is distinguishable. The red arrow points-out at a significantly enhanced spot that may result from unexpected surface roughness. c, d) SHG images of the same set of three

triangular gold nanoprisms obtained with x- and y- polarized excitation. The

typical intensity at the sample was 50 µW at 780 nm.

It is noteworthy that the SHG intensities of the structures can vary from structure to structure due to a probable inhomogeneous distribution of the apex dimensions of the prisms.

As highlighted in Figure 4-5b, some prisms shows SHG confinement while others appear SHG inactive. Polarized measurements are represented in Figure 4-5c,d for horizontal (x) and vertical (y) polarization inputs, respectively. The detected SHG is the sum of the two APDs with polarization analyses along the x (s) and y (p) directions. In Figure 4-5 c,d are shown the SHG spatially resolved maps for both input polarization, and the triangular

a) b) c) d) E k E k x y x y x y x y

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horizontal input polarization (Figure 4-5c), three SHG spots are observed and correspond to the bases of the prisms. For some structures, coupling between the bases of the two upper prisms yields a more elongated SHG activity along the x direction. When the excitation is switched to a vertical polarization, the three SHG spots correspond to the apices of the triangles as shown in Figure 4-5d.

Electromagnetic modeling on the same sets of nanoprisms for Horizontal and Vertical polarizations of input laser beam are shown in Figure 4-6 a-d and e-h for excitations wavelength set at 780 and 850 nm respectively.

Figure 4-6 a, b and e, f display the normalized polarized electric field distributions over a single structure at 780 nm and 850 nm excitation wavelengths, respectively, while Figure 4-6 c, d and Figure 4-6 g, h show the polarized distributions at 390 and 425 nm,

respectively. Control via polarization of the excitation allows to selectively excite

localized plasmons at the distinct directions of the triangular structures (Figure 4-6 a, b, e, f,). For both polarizations and both fundamental wavelengths, an enhancement of the electric field by a factor of ~10 is observed in the vicinity of the apexes of the triangular nanoprisms. Confinement of the SHG at the apices of the triangles is also observed for the second harmonic at 390 and 425 nm, but interestingly the confinement of the SHG at the apices is more prominent at 425 nm (Figure 4-6 g, h) while delocalization of the SHG is observed along the edges of the prisms at 390 nm. Furthermore, the control over the polarization of the excitation allows one to control the position of the resonance at the base of the triangle (x-polarized input) or at the upper apex (y-polarized input) thus yielding distinctive spatial plasmon coupling of the individual structures for both selected polarizations. Remarkably, the obtained images of the electric near-field distribution demonstrate excellent correlation between the observed SHG images reported in Figure 4-5 c, d and the electric charges distribution. It can be inferred therefrom that for a vertical polarization, charges are accumulating in the apices of triangles, whereas for a horizontal one, they concentrate in the base angles.

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nm (Figure 4-6 g, h) confirm the agreement between the observed SHG and LSPR generation. Here again, SHG localization is expected to take place at the apices of the triangles and depends on the input polarization.

Note that in Figure 4-6 c, d, g, h, the non-normalized SHG emission can be correlated with the location of the LSP at 780 and 850 nm. The excitation of the LSP of a metallic feature deprived of centre of symmetry yields efficient SHG that is originating from the same local area as that of the fundamental LSP resonance. The deviations in our observed SHG images from predictions of simulations can be accounted for by the deviation of the real sample geometry from its ideal shape, whereas the observed surface heterogeneities could be ascribed to the surface roughness.

Figure 4-6: Calculations of the electric field distributions in the vicinity of the gold

nanostructures using FDTD calculations. a) Normalized electrical field |E/E0| at

λexcitation=780 nm with x-polarized input. b) Normalized electrical field |E/E0| at

λexcitation=780 nm with y-polarized input. Non-normalized SHG electrical field |E|

calculated at 390 nm for x- (c) and y- (d) polarizations. e) Normalized electrical field

|E/E0| at λexcitation =850 nm with x-polarized input. f) Normalized electrical field

|E/E0| at λexcitation =850 nm with y-polarized input. Non-normalized SHG electrical

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structures appear to be more active presumably due to some local defects responsible for further free electron density increase, thereby enhancing the SHG response. Another possible explanation is the role of the surface roughness associated with the electron- beam evaporation of gold. A measured roughness of 1 nm RMS may be responsible for surface effects that can yield hot-spot areas. A similar phenomenon was reported earlier.41